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The largest natural number n such that 3n divides 66 is... | (Mathematics) | DivineJEE

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Mathematics

Exam

Mathematics

The largest natural number $n$ such that $3^{n}$ divides $66 !$ is ___________.

Explanation

We have,

$\begin{aligned} & {\left[\frac{66}{3}\right]=22} \\ & {\left[\frac{66}{3^2}\right]=7} \\ & {\left[\frac{66}{3^3}\right]=2} \end{aligned}$

Highest powers of 3 is greater than 66. So, their g.i.f. is always 0.

$\therefore$ Required natural number $=22+7+2=31$

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